Final answer:
The essential information needed to find the length of the longest side with a perimeter of 284 units is the length of the other sides. This allows you to subtract their sum from the total perimeter to discover the length of the longest side.
Step-by-step explanation:
In answering the question, in finding the length of the longest side with a perimeter of 284 units, the essential information needed is d) the length of the other sides.
To solve for the length of the longest side of a polygon, knowing the perimeter alone is not sufficient, as the perimeter is the sum of all sides. If the lengths of the other sides are known, you can subtract their total from the perimeter to find the remaining side, which could be the longest. For example, a farmer measuring a four-sided plot and knowing three sides would subtract the sum of those sides from the total perimeter to find the fourth side (mentioned in point 22). This method does not require knowing the angles, diagonals, width, or height specifically, unless those measurements are part of calculating the lengths of the known sides.
Considering the perimeter of a square is 4 times the length of one side, and the area is the square of the side length, these relationships among dimensions help in making such calculations. But when dealing with the longest side of an irregular polygon, the key to finding its length rightly lies in knowing the lengths of all the other sides.